Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio.
This is Value Learning, Part 15: Reward uncertainty, published by rohinmshah.
Crossposted from the AI Alignment Forum. May contain more technical jargon than usual.
In my last post, I argued that interaction between the human and the AI system was necessary in order for the AI system to “stay on track” as we encounter new and unforeseen changes to the environment. The most obvious implementation of this would be to have an AI system that keeps an estimate of the reward function. It acts to maximize its current estimate of the reward function, while simultaneously updating the reward through human feedback. However, this approach has significant problems.
Looking at the description of this approach, one thing that stands out is that the actions are chosen according to a reward that we know is going to change. (This is what leads to the incentive to disable the narrow value learning system.) This seems clearly wrong: surely our plans should account for the fact that our rewards will change, without treating such a change as adversarial? This suggests that we need to have our action selection mechanism take the future rewards into account as well.
While we don’t know what the future reward will be, we can certainly have a probability distribution over it. So what if we had uncertainty over reward functions, and took that uncertainty into account while choosing actions?
Setup
We’ve drilled down on the problem sufficiently far that we can create a formal model and see what happens. So, let’s consider the following setup:
The human, Alice, knows the “true” reward function that she would like to have optimized.
The AI system maintains a probability distribution over reward functions, and acts to maximize the expected sum of rewards under this distribution.
Alice and the AI system take turns acting. Alice knows that the AI learns from her actions, and chooses actions accordingly.
Alice’s action space is such that she cannot take the action “tell the AI system the true reward function” (otherwise the problem would become trivial).
Given these assumptions, Alice and the AI system act optimally.
This is the setup of Cooperative Inverse Reinforcement Learning (CIRL). The optimal solution to this problem typically involves Alice “teaching” the AI system by taking actions that communicate what she does and does not like, while the AI system “asks” about parts of the reward by taking actions that would force Alice to behave in different ways for different rewards.
Does this solve our problems?
Two of the problems we identified in the last post are simply assumed away:
Alice does not know the “true” reward function, but we assumed that she does.
Alice may be unable to optimally give feedback to the AI system, but we assume that she is optimal here.
So this particular kind of reward uncertainty does not fix either of these problems. What about convergent instrumental subgoals?
Utility preservation. One major worry we had with the original setup was that the AI system would disable its narrow value learning system, as a manifestation of the instrumental goal of protecting its utility function. This is reversed in our setup: the AI system has a positive incentive to continue doing narrow value learning, since it helps it hone in on the true reward function, which in turn allows it to optimize the reward better. (We might worry that this prevents us from fixing any problems in the narrow value learning system, but that is a robustness problem: in the world where everything is working correctly, this is the correct incentive.)
Survival incentive, aka shutdown incorrigibility. Another worry is that the AI system has a survival incentive that causes it to prevent us from shutting it down. With reward uncertainty, the fact that we are trying to shut the AI system down is itself strong evidence about...